A reduction cut shortens a limb to a lateral branch large enough.
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The labels for each leaf show which of the abalone sex categories has the highest representation within that part of the sample.
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Decision tree.
A heading cut trims a branch back to a bud, or trims a branch or leader back to a small branch not large enough to assume the growth of the pruned branch.
A decision tree is pruned to get (perhaps) a tree that generalize better to independent test data. (We may get a decision tree that might perform worse on the training data but generalization is the goal). See Information gain and Overfitting for an example. Sometimes simplifying a decision tree gives better results. In machine learning and data mining, pruning is a technique associated with decision trees. Pruning reduces the size of decision trees by removing parts of the tree that do not provide power to classify instances.
Decision trees are the most susceptible out of all the machine learning algorithms to overfitting and effective pruning can reduce this likelihood.